Preheat convection oven to 350°F (preferred) or regular oven to 400°F.
Sprinkle work surface lightly with flour and place dough disc on top, then sprinkle dough lightly with flour. Roll out to 11" diameter and transfer to pie plate. Trim overhang and crimp edges.
Refrigerate for 15 minutes.
Place large parchment paper round over the crust and press lightly into the bottom edge, then fill with pie weights or dried beans to weigh down.
Bake crust for 20 minutes.
Reduce convection oven to 325°F or regular oven to 350°F.
Carefully remove paper & weights, then return crust to oven for 10 minutes until light golden brown.
While crust is finishing, whisk eggs with green onions, heavy cream, salt, & pepper.
Drop onion & tomato mixture across the bottom of the parbaked crust. Top with mozzarella & parmesan, then pour egg mixture evenly on top.
Bake for 35-40 minutes until top is light golden brown. The center should be set but still jiggly.
Cover lightly with foil and let rest for 10 minutes before serving.